Lect35_PathIntegrals

Lect35_PathIntegrals - Double Slit Experiment Consider a...

This preview shows pages 1–3. Sign up to view the full content.

Lecture 35: Path Integral formulation of quantum mechanics PHY851 Quantum Mechanics I Fall, 2008 M.G. Moore Double Slit Experiment Consider a particle which passes through a single slit, then a double slit, and finally is detected by a screen: ) ( 1 d A ) ( 2 d A d 2 2 1 ) ( ) ( 2 1 ) ( d A d A d P + = s n ikL n e d A = ) ( a a 2 2 2 2 1 ) ( d s a s a L ! + + + = s 2 2 2 2 2 ) ( d s a s a L + + + + = P ( d ) = 1 + cos k a 2 + ( s + d ) 2 " 2 + ( s " d ) 2 ( ) ( ) ! " # \$ % & + a sd k d P 2 cos 1 ) ( ! >> d s a , ) ( d P

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Continuum limit Lets add many more screens, and give each many more slits: In the limit of an infinite number of screens with an infinite number of holes per screen, we recover the case of no screens at all Thus the free propagation of the particles wave- function can be computed by summing the appropriate path-amplitude over all possible paths 2 1 ) ( ! = paths j paths A N d P Formal approach Suppose a particle is at position at time t 0 =0. The probability amplitude to be at position at later time t is then clearly given by QM to be: This is called the QM ‘Propagator’ If we know the initial state, we can thus compute the state at any later time as
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

Page1 / 6

Lect35_PathIntegrals - Double Slit Experiment Consider a...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online